What type of free, democratic society would exempt its public officials, including its highest elected official, from criminal investigation and indictment while in office?

An article in The New York Times by Adam Liptik dated May 29, 2017, says the closest the Constitution comes to addressing the issue is in Article 1 Section 3 that addresses the outcome of impeachment which “shall not extend further than to removal from office, and disqualification to hold and enjoy any office of honor, trust or profit under the United States.” But then it also goes on to say: “But the party convicted shall nevertheless be liable and subject to indictment, trial, judgement and punishment, according to law.”